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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 03 Dec 2017 14:18:14 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/03/t15123071616wdtlzxjw3tmbna.htm/, Retrieved Tue, 14 May 2024 01:19:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308451, Retrieved Tue, 14 May 2024 01:19:55 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

103

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [] [2017-12-03 13:18:14] [834c75312b1a933b06457deba9c9b5e8] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308451&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

2 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308451&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308451&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.899502	13.0969	0
2	0.874235	12.7291	0
3	0.876462	12.7615	0
4	0.82099	11.9538	0
5	0.84735	12.3376	0
6	0.85555	12.457	0
7	0.807662	11.7597	0
8	0.789631	11.4972	0
9	0.798066	11.62	0
10	0.764679	11.1339	0
11	0.787908	11.4721	0
12	0.812807	11.8347	0
13	0.741844	10.8014	0
14	0.732291	10.6623	0
15	0.707635	10.3033	0
16	0.665642	9.6919	0
17	0.698989	10.1774	0
18	0.689152	10.0342	0
19	0.652757	9.5043	0
20	0.649604	9.4584	0
21	0.634102	9.2327	0
22	0.618319	9.0029	0
23	0.64876	9.4461	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.899502 & 13.0969 & 0 \tabularnewline
2 & 0.874235 & 12.7291 & 0 \tabularnewline
3 & 0.876462 & 12.7615 & 0 \tabularnewline
4 & 0.82099 & 11.9538 & 0 \tabularnewline
5 & 0.84735 & 12.3376 & 0 \tabularnewline
6 & 0.85555 & 12.457 & 0 \tabularnewline
7 & 0.807662 & 11.7597 & 0 \tabularnewline
8 & 0.789631 & 11.4972 & 0 \tabularnewline
9 & 0.798066 & 11.62 & 0 \tabularnewline
10 & 0.764679 & 11.1339 & 0 \tabularnewline
11 & 0.787908 & 11.4721 & 0 \tabularnewline
12 & 0.812807 & 11.8347 & 0 \tabularnewline
13 & 0.741844 & 10.8014 & 0 \tabularnewline
14 & 0.732291 & 10.6623 & 0 \tabularnewline
15 & 0.707635 & 10.3033 & 0 \tabularnewline
16 & 0.665642 & 9.6919 & 0 \tabularnewline
17 & 0.698989 & 10.1774 & 0 \tabularnewline
18 & 0.689152 & 10.0342 & 0 \tabularnewline
19 & 0.652757 & 9.5043 & 0 \tabularnewline
20 & 0.649604 & 9.4584 & 0 \tabularnewline
21 & 0.634102 & 9.2327 & 0 \tabularnewline
22 & 0.618319 & 9.0029 & 0 \tabularnewline
23 & 0.64876 & 9.4461 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308451&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.899502[/C][C]13.0969[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.874235[/C][C]12.7291[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.876462[/C][C]12.7615[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.82099[/C][C]11.9538[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.84735[/C][C]12.3376[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.85555[/C][C]12.457[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.807662[/C][C]11.7597[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.789631[/C][C]11.4972[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.798066[/C][C]11.62[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.764679[/C][C]11.1339[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.787908[/C][C]11.4721[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.812807[/C][C]11.8347[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.741844[/C][C]10.8014[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.732291[/C][C]10.6623[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.707635[/C][C]10.3033[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.665642[/C][C]9.6919[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.698989[/C][C]10.1774[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]0.689152[/C][C]10.0342[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]0.652757[/C][C]9.5043[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]0.649604[/C][C]9.4584[/C][C]0[/C][/ROW]
[ROW][C]21[/C][C]0.634102[/C][C]9.2327[/C][C]0[/C][/ROW]
[ROW][C]22[/C][C]0.618319[/C][C]9.0029[/C][C]0[/C][/ROW]
[ROW][C]23[/C][C]0.64876[/C][C]9.4461[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308451&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308451&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.899502	13.0969	0
2	0.874235	12.7291	0
3	0.876462	12.7615	0
4	0.82099	11.9538	0
5	0.84735	12.3376	0
6	0.85555	12.457	0
7	0.807662	11.7597	0
8	0.789631	11.4972	0
9	0.798066	11.62	0
10	0.764679	11.1339	0
11	0.787908	11.4721	0
12	0.812807	11.8347	0
13	0.741844	10.8014	0
14	0.732291	10.6623	0
15	0.707635	10.3033	0
16	0.665642	9.6919	0
17	0.698989	10.1774	0
18	0.689152	10.0342	0
19	0.652757	9.5043	0
20	0.649604	9.4584	0
21	0.634102	9.2327	0
22	0.618319	9.0029	0
23	0.64876	9.4461	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.899502	13.0969	0
2	0.341186	4.9677	1e-06
3	0.305259	4.4446	7e-06
4	-0.142737	-2.0783	0.019443
5	0.337655	4.9163	1e-06
6	0.15919	2.3178	0.010706
7	-0.135319	-1.9703	0.025054
8	-0.184725	-2.6896	0.003861
9	0.247521	3.604	0.000195
10	-0.035048	-0.5103	0.305182
11	0.143963	2.0961	0.018629
12	0.14499	2.1111	0.017968
13	-0.28424	-4.1386	2.5e-05
14	-0.146538	-2.1336	0.017011
15	-0.10588	-1.5416	0.062328
16	0.020103	0.2927	0.385019
17	0.098068	1.4279	0.077398
18	0.017288	0.2517	0.400749
19	0.00613	0.0893	0.46448
20	0.007111	0.1035	0.458819
21	0.030365	0.4421	0.329426
22	0.055278	0.8049	0.210903
23	0.06007	0.8746	0.191381

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.899502 & 13.0969 & 0 \tabularnewline
2 & 0.341186 & 4.9677 & 1e-06 \tabularnewline
3 & 0.305259 & 4.4446 & 7e-06 \tabularnewline
4 & -0.142737 & -2.0783 & 0.019443 \tabularnewline
5 & 0.337655 & 4.9163 & 1e-06 \tabularnewline
6 & 0.15919 & 2.3178 & 0.010706 \tabularnewline
7 & -0.135319 & -1.9703 & 0.025054 \tabularnewline
8 & -0.184725 & -2.6896 & 0.003861 \tabularnewline
9 & 0.247521 & 3.604 & 0.000195 \tabularnewline
10 & -0.035048 & -0.5103 & 0.305182 \tabularnewline
11 & 0.143963 & 2.0961 & 0.018629 \tabularnewline
12 & 0.14499 & 2.1111 & 0.017968 \tabularnewline
13 & -0.28424 & -4.1386 & 2.5e-05 \tabularnewline
14 & -0.146538 & -2.1336 & 0.017011 \tabularnewline
15 & -0.10588 & -1.5416 & 0.062328 \tabularnewline
16 & 0.020103 & 0.2927 & 0.385019 \tabularnewline
17 & 0.098068 & 1.4279 & 0.077398 \tabularnewline
18 & 0.017288 & 0.2517 & 0.400749 \tabularnewline
19 & 0.00613 & 0.0893 & 0.46448 \tabularnewline
20 & 0.007111 & 0.1035 & 0.458819 \tabularnewline
21 & 0.030365 & 0.4421 & 0.329426 \tabularnewline
22 & 0.055278 & 0.8049 & 0.210903 \tabularnewline
23 & 0.06007 & 0.8746 & 0.191381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308451&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.899502[/C][C]13.0969[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.341186[/C][C]4.9677[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.305259[/C][C]4.4446[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]-0.142737[/C][C]-2.0783[/C][C]0.019443[/C][/ROW]
[ROW][C]5[/C][C]0.337655[/C][C]4.9163[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.15919[/C][C]2.3178[/C][C]0.010706[/C][/ROW]
[ROW][C]7[/C][C]-0.135319[/C][C]-1.9703[/C][C]0.025054[/C][/ROW]
[ROW][C]8[/C][C]-0.184725[/C][C]-2.6896[/C][C]0.003861[/C][/ROW]
[ROW][C]9[/C][C]0.247521[/C][C]3.604[/C][C]0.000195[/C][/ROW]
[ROW][C]10[/C][C]-0.035048[/C][C]-0.5103[/C][C]0.305182[/C][/ROW]
[ROW][C]11[/C][C]0.143963[/C][C]2.0961[/C][C]0.018629[/C][/ROW]
[ROW][C]12[/C][C]0.14499[/C][C]2.1111[/C][C]0.017968[/C][/ROW]
[ROW][C]13[/C][C]-0.28424[/C][C]-4.1386[/C][C]2.5e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.146538[/C][C]-2.1336[/C][C]0.017011[/C][/ROW]
[ROW][C]15[/C][C]-0.10588[/C][C]-1.5416[/C][C]0.062328[/C][/ROW]
[ROW][C]16[/C][C]0.020103[/C][C]0.2927[/C][C]0.385019[/C][/ROW]
[ROW][C]17[/C][C]0.098068[/C][C]1.4279[/C][C]0.077398[/C][/ROW]
[ROW][C]18[/C][C]0.017288[/C][C]0.2517[/C][C]0.400749[/C][/ROW]
[ROW][C]19[/C][C]0.00613[/C][C]0.0893[/C][C]0.46448[/C][/ROW]
[ROW][C]20[/C][C]0.007111[/C][C]0.1035[/C][C]0.458819[/C][/ROW]
[ROW][C]21[/C][C]0.030365[/C][C]0.4421[/C][C]0.329426[/C][/ROW]
[ROW][C]22[/C][C]0.055278[/C][C]0.8049[/C][C]0.210903[/C][/ROW]
[ROW][C]23[/C][C]0.06007[/C][C]0.8746[/C][C]0.191381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308451&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308451&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.899502	13.0969	0
2	0.341186	4.9677	1e-06
3	0.305259	4.4446	7e-06
4	-0.142737	-2.0783	0.019443
5	0.337655	4.9163	1e-06
6	0.15919	2.3178	0.010706
7	-0.135319	-1.9703	0.025054
8	-0.184725	-2.6896	0.003861
9	0.247521	3.604	0.000195
10	-0.035048	-0.5103	0.305182
11	0.143963	2.0961	0.018629
12	0.14499	2.1111	0.017968
13	-0.28424	-4.1386	2.5e-05
14	-0.146538	-2.1336	0.017011
15	-0.10588	-1.5416	0.062328
16	0.020103	0.2927	0.385019
17	0.098068	1.4279	0.077398
18	0.017288	0.2517	0.400749
19	0.00613	0.0893	0.46448
20	0.007111	0.1035	0.458819
21	0.030365	0.4421	0.329426
22	0.055278	0.8049	0.210903
23	0.06007	0.8746	0.191381

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
par2 <- '1'
par1 <- 'Default'
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,'ACF(k)',header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,'PACF(k)',header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code